Mountain Maths at ISZL


Primary Specialist Neil McCallion explains how ISZL's annual mathematics retreat inspires and motivates learners

Girls using multilink cubes in Maths

Over a decade ago, Mountain Maths began as an elite competition event between Swiss international schools, hosted by ISZL at Chalet Bergheim, Wengen.  Now, Mountain Maths is an ISZL mathematical retreat for all Primary students.  This term, we engaged in Mountain Maths at the ISZL campus.  We may not have been at Wengen, but the mountain became a metaphor for the mathematical challenges Grade 4 students had to face!

The aim of Mountain Maths is to involve and engage students with a broader view of mathematics by presenting many non-routine problems and puzzles.  The tasks are mixed - some are famous recreational maths problems, while others have an interesting historical origin. 

It was important to include geometric problems too, particularly because some students can easily develop the thinking error that being slick with number makes you a great mathematician. In fact, mathematics is all about patterns and relationships.  

Here’s a taste of the mathematics Grade 4 students and teachers engaged with. Click on the blue title for further information:

The Code Breakers

Eight multiplication tables are presented in code.  Students use logic and reasoning and knowledge of multiplication facts, to decipher the coded tables.

Here we see the 3 x table.  Initially quite baffling to many students, gradually, particular observations guide their thinking:

A teacher shows students a times table in code


  • It has three single digit products
  • E x A = E, so A must be 1
  • E x AC = EC, so AC must be 10
  • E x D = FA..A equals 1 so F is 2 and D is 7
  • There’s only one product that ends in 1 in the 3 times table!



Building on prior learning at ISZL, students were reminded of pentominoes, 5 squares joined side to side.  There are 12 discrete pentominoes.  The next challenge: Find all possible hexominoes (there are 35 possibilities).

Boy stands at board with Hexominoes


9 colour cube puzzle

27 cubes, 9 colours. The problem - arrange the 27 cubes so all 9 colours are visible on every face.

Girl doing archery

Archery: target practice with mental arithmetic!


The Handshake Problem
A classic recreational maths problem that is rich in patterns and relationships. There were 120 handshakes at a business meeting. How many people were at the meeting?


Orienteering in the school grounds
Students had to find up to 22 locations and solve a maths problem at each one...mental mathematics combined with exercise and map reading. Thanks to Neil Sanders for providing the orienteering route.

Neil McCallion with students

Students consider their orienteering route

The persistence and engagement of the Grade 4 students was excellent throughout Mountain Maths, and I am sure there are many who will want to return to problems yet unsolved!


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